On a wood arrow shaft, runout is where the grain runs off the shaft.
Unless the grain on the shaft is perfectly straight you'll see "points" on the shaft where the grain runs off.
The theory is if the arrow were to break upon release, it could break along the grain lines. With the runout on top and pointed to the tip the rear of the broken arrow should go up and away from the bow hand.
I opened a thread a few weeks ago asking if anyone had actually seen an arrow break along these grain lines. The consensus was that while none of us had actually seen an arrow break in this manner, we would still orient the grain like this just as a matter of uniformity, if nothing else.
It may be amusing to note that 4-fletch shooters have a 50/50 chance of putting their arrow on "upside down."
Guy